THE EVOLUTION OF SATELLITES. 115 



united by a bar. The outcome of the lunar tidal friction will therefore 

 be that the moon and the earth will go round as though locked together 

 in a period of fifty-five of our present days, with day and month identi- 

 cal in length. 



Now, looking backward in time, we find the day and the month short- 

 ening, but the day changing more rapidly than the month. The earth 

 was therefore able to complete more revolutions in the month, although 

 that month was itself shorter than it is now. We get back, in fact, to 

 a time when there were twenty -nine rotations of the earth in the time 

 of the moon's revolution, instead of twenty-seven and one-third, as at 

 present. This epoch is a sort of crisis in the history of the moon and 

 the earth, for it may be proved that there never could have been more 

 than twenty-nine days in the month. Earlier than this epoch, the 

 days were fewer than twenty-nine; and later, fewer also. Although 

 measured in years this epoch in the earth's history must be very 

 remote, yet when we contemplate the whole series of changes it must 

 be considered as a comparatively recent event. In a sense, indeed, we 

 may be said to have passed recently through the middle stage of our 

 history. 



Now, pursuing the series of changes farther back than the epoch 

 when there was the maximum number of days in the month, we find 

 the earth still rotating faster and faster and the moon drawing nearer 

 and nearer to the earth and revolving in shorter and shorter periods. 

 But a change has supervened, so that the rate at which the month is 

 shortening is more rapid than the rate of change in the day. Conse- 

 quently, the moon now gains, as it were, on the earth, which can not 

 get round so frequently in the mouth as it did before. In other words, 

 the number of days in the month declines from the maximum of twenty- 

 nine, and is finally reduced to one. When there is only one day in the 

 month the earth and the moon go round at the same rate, so that the 

 moon always looks at the same side of the earth, and as far as concerns 

 the motion they might be fastened together by iron bands. 



This is the same conclusion at which we arrived with respect to the 

 remote future. But the two cases differ widely; for whereas in the 

 future the period of the common rotation will be fifty-five of our j)res- 

 ent days, in the past we find the two bodies going round each other in 

 between three and five of our present hours. A satellite revolving 

 round the earth in so short a period must almost touch the earth's sur- 

 face. The system is therefore traced until the moon nearly touches the 

 earth, and the two go round each other like a single solid body in 

 about three to five hours. 



The series of changes has been traced forward and backward from 

 the present time, but it will make the whole process more intelligible, 

 and the opportunity will be aftbrded for certain further considerations, 

 if I sketch the history again in the form of a continuous narrative. 



Let us imagine a planet attended by a satellite which revolves in a 



